Band-pass filter, including trap circuit



July 1, 1941- H. A. WHEELER BAND-PASS FILTER INCLUDING TRAP CIRCUITFiled Sept. 29, 1959 2 Sheets-Sheet 1 g E0 3, o n f: 1E: Frequency.

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INVENTOR HAROLD A.WHEELER BYf ATTORN EY y 1941- H. A. WHEELER 2,247,898v

BAND-PASS FILTER INCLUDING TRAP CIRCUIT Filed Sept. 29, 1939 2Sheets-Sheet 2 INVENTOR HAROLD A. WH EELE R vmm/ ATTORNEY Patented July1, 1941 2,247,898 BAND-PASS FILTER, INCLUDING TRAP CIRCUIT Harold A.Wheeler, Great Neck, N. Y., assignor to Hazcltine Corporation, acorporation of Dela ware Application September 29, 1939, Serial No.297,081

19 Claims.

This invention relates to band-pass filters including filter sectionshaving trap circuits therein and having an image impedance at a pair ofterminals which has opposite extreme values at the upper and lowercutoff frequencies of the pass band. While the filters of the inventionare of general application, they are of particular utility in effectingan impedance transformation between two pairs of terminals whileproviding traps for frequencies just outside of a desired continuouspass band.

A double-tuned transformer is a commonly used form of band-pass filtersection. Such a transformer circuit may be regarded as two halfsectionsjoined together, each comprising a shuntand a series-reactance arm. Eachof these half-sections comprises at their junction a pair of terminalsacross which the image impedance has opposite extreme values at theupper and lower cutoff frequencies of the pass band, which form of imageimpedance is not matched with the more familiar constant-k type ofbandpass image impedance. However, such filter half-sections have manyuses and are of particular utility because oftheir extreme simplicityand their image-impedance transforming properties between their tWopairs of terminals. Band-pass filters utilizing only half-sections ofthe type under discussion, or such half-sections in combination withother known filter sections, have the disadvantage that, for somepurposes, sufiicient attenuation at frequencies just above and below thepass band is not secured with a minimum number of circuit elements. Thisis true, even if the other known filter sections are of types includingtrap circuits to provide maximum attenuation at particular frequenciesoutside the pass band. Some attempts to design simple filters with trapshave yielded filters with spurious pass bands in addition to the desiredpass band, and such spurious bands are usually undesirable.

It is an object of the present invention, therefore, to provide animproved impedance-transforming band-pass filter half-section whichincludes a trap for frequencies outside the pass band.

It is another object of the invention to provide an improved band-passfilter half-section which passes only a single continuous band and whichincludes a trap circuit for frequencies outside the pass band.

It isanother object of the invention to provide an improved band-passfilter section for passing a single band of frequencies and whichincludes a trap circuit for frequencies above the pass band and a trapcircuit for frequencies below the pass band.

It is still another object of the'invention to provide a band-passfilter network for passing a single continuous band of frequencies whichincludes one or more trap circuits for frequencies outside of the passband and which tolerates maximum shuntcapacitance across one or bothpairs of terminals.

In accordance with one feature of the invention, a band-pass filterhalf-section having in put and output pairs of terminals effectivelycomprises seriesand shunt-reactance arms of which at least each of twoincludes a portion individually of the same reactance-frequencycharacteristic and of a given kind of reactance at frequencies withinthe passband; that is, all such portions individually hav the samevariation of reactance with frequency over the pass band and effectivelyprovide either only inductive or only capacitivereactance at frequencieswithin the pass band. A trap circuit is included in one of thereactancearms which is adjacent to one of the pairs of terminals andcomprises the only other reactance of the half-section. The trap circuitis resonant at a. frequency outside of the pass band andis so connectedto present reactance of the kind opposite to that of the said portionsat frequencies within the pass band, whereby the image impedance at theother pair of terminals is caused to present opposite extreme valuesatthe upper and lower cutoff frequencies of the pass band.

In accordance with another feature of the invention, a band-pass filtersection has input and output pairs of terminals and effectivelycomprises, seriesand shunt-reactance arms at least each of three ofwhich includes a portion of the same reactance-frequency characteristicand of a given kind at frequencies in the pass band; the filter sectionalso includes a trap circuit in on of its reactance arms which isconnected between two of the said three reactance arms and whichcomprises the only other reactance of the filter section. The trapcircuit is resonant at a frequency outside of the pass band and presentsreactance of the kind opposite to that of the above-mentioned portions.at frequencies in the pass band, whereby the image impedance at bothpairs of terminals is caused to have opposite extreme values at theupper and lower frequencies of the pass band.

In accordance with another feature of the invention, aconfiuentband-pass filter effectively comprises a series of filter half-sectionswith image-impedance matching at their junctions, each of two adjacentones of said half-sections having both seriesand shunt-reactance arms ofwhich each of two of the reactance arms adjacent to their junctionincludes a portion individually of the samereactance-frequencycharacteristic and of a given. kind of reactance at frequencies in thepass band. The filter of this embodiment also includes a trap circuit ineach of the said two adjacent half-sections which is removed from theirjunction by at least one of the said adjacent reactance arms and whichcomprises the only other reactance of th half-sec tion. One of the trapcircuits comprises a shunt arm of series-connected capacitance andinduct ance resonant at a frequency on one side of the pass band, andthe other of the trap circuits comprises a series arm havingparallel-connected capacitance and inductanc resonant at a frequency onthe other side of the pass band. The matched image impedance at theabove-mentioned junction therefore has opposite extreme yalues at theupper and lower cutoff frequencies of the pass band and unlike trapcircuits are provided in the two adjacent half-sections.

In accordance with still another feature of the invention, a band-passfilter comprises two resonant circuits each having an inductor coupledtherewith by mutual inductance, a series circuit including the saidinductors and a trap circuit with parallel-connected capacitance andinductance resonant at a frequency below the pass band, and a secondtrap circuit connected in parallel with one of the above-mentionedinductors and including series-connected capacitance and inductanceresonant at a frequency above the pass band. The filter is preferablyproportioned to pass a continuous band of frequencies and to securemaximum attenuation at frequencies above and below the pass band.

It is seen, therefore, that, while some arrangements of the prior artutilize both a band-pass filter circuit and. one or more trap circuitsfor frequencies outside the pass band of the filter, such prior artarrangements are subject to the disadvantage that they require more thanthe minimum number of circuit elements or the filter properties of thefilter are disturbed by the addition of the trap circuit. In the lattercase, the filter may be caused to have one or more spurious pass bandsother than the desired pass band. The invention, however, provides amost simple bandpass filter which effectively includes the requirednumber of trap circuits with filtering properties undisturbed by theinclusion of the traps. Substantially only one single continuous band offrequencies is passed by the filter circuits of the invention.

For a better understanding of the invention, together with other andfurther objects thereof, reference is had to the following descriptiontaken in connection with the accompanying drawings, and its scope willbe pointed out in the appended claims.

Each of Figs. 1a. and 1b of the drawings represents a filterhalf-section which is equivalent to one-half of a double-tunedtransformer circuit and which is utilized to explain the principles ofoperation of the present invention; Fig. 1c is a graph of theimage-impedance characteristic at one pair of terminals of each of thecircuits of Figs. la and 1b, which characteristic is similar to theimage-impedance characteristic at one pair of terminals of each of thefilter half-sections of the invention; each of Figs. 2a and 2b is acircuit diagram of a band-pass filter half-section of the inventioncomprising a trap circuit for frequencies below the pass band; each ofFigs. 3a and 32: represents a band-pass filter half-section of theinvention comprising a trap circuit for frequencies above the pass band;Fig. 4a is a circuit diagram of a band-pass filter in accordance withthe invention which is utilized to couple two vacuum tubes in cascadeand which comprises a trap circuit for frequencies above the pass bandof the system; Figs. ib-4e, inclusive, represent equivalentmodifications of the circuit of Fig. 4a; Fig. 5a is a circuit diagram ofa band-pass filter in accordance with the invention which comprises atrap circuit for frequencies above the pass band and a trap circuit forfrequencies below the pass band; each of Figs. 5b to 5e, inc.,represents an equivalent modification of the circuit of Fig. 5a.

Referring now more particularly to Fig. la of the drawings, there isshown a filter half-section comprising a shunt reactance arm includingparallel-connected inductance L and capacitance C1 and aseries-reactance arm including inductance L2. The filter half-section ofFig. 1a is a known electrical equivalent of one-half a filterwhole-section comprising a conventional doubletuned transformer. Thefilter comprises one pair of input terminals I, I across which appearsthe image impedance of nominal value R1 and another pair of inputterminals 2, 2 across which appears the image impedance R2. Theconventional double-tuned transformer circuit may also be divided in aknown manner into two filter halfsections of the form shown in Fig. 1b,each of Which includes a shunt-reactance arm comprising capacitance C1across terminals I, I, a seriesreactance arm comprising inductance L3,and a shunt-reactance arm comprising inductance L4 connected acrossterminals 2, 2. Each of the following equations is applicable to one orboth of the circuits of Figs. 1a and 1b:

Zz' image impedance at terminals 2, 2 of Fig. 1b;

fm the mean frequency of the pass band;

wz=the angular frequency at the lower cutoff frequency;

wa=the angular frequency at the upper cutoff frequency;

Ri=noinilnal image impedance across terminals Rz nominal image impedanceacross terminals 2, 2 of Fig. la;

Rc=nominal image impedance across terminals 2, 2 of Fig. lb.

In Fig. 10 there is illustrated the form of the image-impedancecharacteristic at the terminals 2, 2 of each of the filter half-sectionsof Figs. 1a and lb. Each half-section includes one tuned pass band.

circuit" and has at the terminals l, I .a constant-k mid-shunt impedanceof mid-band valueRi associate'dwith the maximum tolerable shuntcapacitance C1, where From Fig. lc it is seen that the image impedanceacross terminals 2, 2 has opposite extreme values at the cutofffrequencies of the pass band; that is, it is infinite at the lowercutofl' frequency hand zero at the upper cutofi frequency f2, and thistype of image impedance serves as a basis for joining the half-sectionsof further embodiments of the invention in filter networks comprisingadditional filter-sections of different types.

In Fig. 2a there is illustrated a filter half-sectionin accordance-withthe present invention which includes a trap for frequencies below thepass band. This filter half-section includes a shunt-reactance armacross terminals 3, 3 comprising inductance L5 and a series-reactancearm including inductance L6 in series with parallelconnectedtrap-circuit inductance L7 and capacitance C7. The following equationsare applicable to the circuit of Fig.2a:

where, I h h Z3=image impedance at terminals 3, 3;

' f1=resonant frequency of trap circuit L7, C1; 7

w1=angu1ar frequency corresponding to is; and Ra=mid-band imageresistance at terminals 3, 3.

The image-impedance characteristic of thejfilter of Fig. 2a atthe'ter-minals 3, 3 has the same ing inductance L5 and theseries-reactance arm includes a portion com-prising inductance Ls, theportions both having inductive reactance at frequencies in the pass bandand the same react- ;ance at frequencies in the pass band and the samereactance-frequency characteristic. A trap circuit is 'included in theseries-reactance arm which is adjacent to the pair of terminals 4, 4

"and comprises the only other reactance of the half-section. 'Thetrapcircuit is resonant at a frequency below the passband and presentscapacitive reactance, which is of the kind. opposite to that of the saidportions at frequencies inthe half-section of Fig. 31) comprises pairsof ter-,

Another filter half-section in accordance with the present invention,including a trap circuit for frequencies below the pass band and havingthe same cutoff frequencies, is illustrated in Fig. 2b. This filterhalf-section comprises pairs of terminals -5, -5 and 6, 6 and includes aseries-reactance arm comprising inductance La, a shunt-reactance armcomprising inductance L9, and a series arm including parallel connectedinductance Lie-and capacitance C10. The circuit of Fig. 2b is readilyderived from that of Fig. 2a by a simple impedance transformation. 1

The image impedance Z5 at terminals 5, 5 is identical with that atterminals 3, 3 of Fig. 2a. That at terminals 6, 6 has the same form asthat at terminals 4, 4 but a different magnitude.

In Fig. 3a of the drawings there is illustrated a band-pass filterhalf-section in accordance with the invention, including a trap circuitforffrequencies above the pass band. This filter halfsection includes aseries-reactance arm compris- 'ing inductance L11 and a shunt-reactancearm including inductance L12 connected in parallel with series-connectedinductance L1: and capacitance C13, the pairs of terminalsof thefilter'halfsection z-being identified by numerals I, I and 8, 8.

The following equations are applicable to the cir- 7 Zi=iinage impedanceat terminals I, I;

R7=mid-band image resistance at terminals 1, I;

w and F 'w3 ='angular frequency of trap circuit L13, C13.

minals. 9, 9 and III, III, a shunt-reactance arm across terminals 9, 9including inductance L14, a series-reactance arm including inductanceL15, and a shunt reactance arm across terminals i0, i0 includingseries-connected inductance llm and capacitance Cl6.- The circuit ofFig. 3b is vacuum tubes l5 and IS in cascade. The bandpass filtercircuit cf Fig. 40. includes four filter half-sections; they areconnected with'imageimpedance matching at their respective junctionssections to which the opposite terminals of each of the intermediatehalf-sections are connected provide. a constant-k band-pass mid-shuntimage impedance across the input and output terminals. The endhalf-sections and, therefore, the composite filter circuit is of a typewhich tolerates maximum shunt capacitance across the output circuit oftube I5 and across the input circuit of tube Hi. It will be understoodthat the capacitances C20, C20 may be comprised in whole or in part ofthe interelectrode capacitance-s of the tubes to .which they arecoupled. It is also seen that the band-pass filter section, includingthe series-inductance arms L15, L15 of Fig. 4a effectively com-prisesseriesand shunt-reactance arms, of which each of at least three includesportions individually of the same impedancefrequency characteristic andof a given kind of reactance at frequencies within the pass band.Specific-ally, four of the arms individually include inductances L14,L15, L15, and L14, each of which portions has an inductive reactance atfrequencies within the pass band. Furthermore, a trap circuit, includingboth trap circuits L16, C16, is included in the one of the reactancearms of the filter section which is between two of the three inductancearms and comprises the only other reactance of the filter section. Thisresultant trap circuit is resonant at a frequency above the pass bandand presents reactance of the opposite kind, that is, capacitance, atfrequencies within the pass band.

The circuit of Fig. 4b is the full electrical equivalent of that of Fig.4a. and differs only in that adjacent shunt-inductance arms L22 and L14of Fig. 4a have been combined into the single inductance element L25 andthe adjacent seriesinductance arms L21 and L15 have been combined singleshunt-inductance element L28.

The circuit of Fig. 4:2 is identical with that of Fig. 40 except that atransformer including inductively-coupled primary and secondaryinductances Lao, L31 has been substituted for the adjacent inductanceelements L23, L28 of Fig. 4c in a manner which is wellunderstood in theart.

The circuit of Fig, 4c is identical with that of Fig. 4d except that afurther similar transformation has been made to provide an equivalentcircuit including three inductors L31, L32, and L33 each of which iscoupled to each of the others. They are respectively tuned by condensersC31, C32, and C33.

In.-Fig..5a there is illustrated another modification of the inventioncomprising trap circuits resonant at frequencies both below and abovethe pass band which may be utilized for effecting an impedancetransformation between two pairs of terminals. The filter of Fig. 5acomprises all of the elements of the filter -of Fig. 4a. and includes inaddition a filter section comprising two filter half-sections, eachidentical with the half-section of the filter of Fig. 2a. Circuitelements which are similar to those. of Fig. 2a. and Fig. 4a haveidentical reference numerals. The filter section com-prisingg the twohalf-sections similar to that of Fig. 2a is included between one of theend filter half-sections including. elements L21, L22, C20 and theadjacent half-section including a trap circuit which is resonant at afrequency above the pass band. The operation of the circuit of Fig. 50.will be understood from the description which has been given withreference to the individual filter half-sections which form componentparts thereof, rendering a further description unnecessary herein. Asstated above, the image impedance at the terminals 3, 3 of Fig, 2a is ofthe same form as that at terminals 2, 2 of Fig. 1b and the terminals 9,9 of Fig. 3b, so that these filter sections canbe connected in cascadewith image-impedance matching at their junctions.

It is, therefore, seen that the filter circuit of Fig. 5a is a confluentband-pass filter effectively comprising a series of filter half-sectionswith image-impedance'matching at their junctions, each of two adjacent.ones of the half-sections comprising both seriesand shunt-reactancearms of which each of two of the four arms adjacent their junctionincludes a portion individually of the same reactance-frequencycharacteristic and of a given kind of reactance at frequencies in thepass band; specifically, the said two halfsections include inductancesL15, L14 and L5, and L6, each having an inductive reactance atfrequencies in the pass band. A trap circuit is included in each of thetwo adjacent half-sections under discussion which is removed from theirjunction by at least one of the above-mentioned adjacent arms-andcomprises the only other reactance of such half-section. One of the trapcircuits comprises a shunt 'arm of seriesconnected capacitance C16 andinductance L16 resonant at a frequencyion one side of the pass band andthe other trap-circuit comprises a series arm having parallel-connectedcapacitance C7 and inductance L2 resonant at a frequency on the otherside of the-pass band. 1

In Fig. 5b is showna' modification of the filter of Fig.-5a-inwhich'single-trap circuits are substituted for-the two adjacent-trapcircuits of each type in the filter 'of Fig. 5a, adjacent inductanceelements of similar kind being combined in a single inductanceeleme'ntand" impedance transformation being effected between like elements inadjacent arms of opposite type. The circuit of Fig. 5b-thus comprises asingle trap circuit L36, C36 resonant at a frequency above the pass banda single trap circuitLa's; C39 resonant at a frequency below the passband, shunt-inductance elements Lu and L40, and series-inductanceelements Laaand L38,

The circuit of Fig. 5c is identical to that of Fig. 5b except that'anequivalent transformer L42, L114 has been substitutedin a manner wellunderstood in the art for the adjacent inductance elements L31, L 8 ofFig. 5b.

The filter circuit of Fig. 5d is also the .eleccircuits are provided intrical equivalentlof thefilter circuit of Fig. a and is derived from thecircuit of Fig. 5a by combining adjacent inductance elements, combiningeach of the two pairs of trap circuits into a single pairof trapcircuits, and effecting an impedance transformation. The filter ofFig.'5d thus comprises a single trap circuit L51, C51 resonant at afrequency above the pass band, a single trap circuit L53,- C53 resonantat a frequency below the pass band, series-inductance elements L56 andL57, and shunt-inductance elements L50 and Len The filter circuit ofFig. 5e is similar to that of Fig. 5d except that an equivalenttransformer L60, L61 has been. substituted for the adjacent inductanceelements 1150,1156 of Fig. 5d and a second transformer L64, Lesha's beensubstituted for the adjacent inductance elements L54, L51 of Fig. 5d ina manner well understood in the art.

It is apparent that the band-pass filter of Fig. 5e comprises tworesonant circuits L60, C20 and L65, 020 having inductors L61 and L64individually coupled therewith by mutual inductance. The filtercomprises a series circuit including the inductors'Lsi, L64 and a trap'circuit with parallelconnected capacitance C53 and inductance L53resonant at a frequency below the pass band. The filter also'comprises asecond trap circuit connectedin parallel with inductor L61 includingseries-connected capacitance'csi and inductance Lsiresonant at afrequency above the pass band,

whereby a single continuous band of frequencies is caused to be'passedby the filter and maximum attenuation is'secured at the resonantfrequencies of the trap circuits above and below the pass band.

While therei'have been described what are at presentrconsidered to bethe preferred embodiments of this invention, it will be obvious to thoseskilled in the art that various changes and modificationssmay be madetherein without departing from-the invention, and it is, therefore,aimed in the appended claims to cover all such changes andimodificationsas fall within the true spirit and scope of the invention.

' What is claimed is:

1. A confluent band-pass filter effectively comprising, a series offilter half-sections with imageimpedance matching at their junctions,each of two 'adjacent'ones of said half-'sectionshaving both'seriesandshunt-reactance arms of which 'each'of two of said arms adjacent theirjunction includes aportion individually of the same reactance-frequencycharacteristic and of a given kindof reactance at frequencies within thepass band,"a' trap circuit included in each of said twoadjacent'half-sections and removed from said junction by at least one'of'said adjacent reactance arms and comprising the only other reactance ofthe half-section, one of said trap circuits comprising a shunt arm ofseries-connected capacitance and inductance reson'ant'at afrequencyonone side of the pass band, 'and the *otherof said trapcircuits comprising a series arm having parallel-connected capacitanceand inductance resonant at a frequency on the other side of the passband, whereby the matched image impedance at said junction is caused tohave opposite extreme values at the upper and lower cutoff frequenciesof the pass band and unlike trap the said two adjacent half-sections.

2.A confluent band-pass filter effectively com- "prising, a series offilter half-sections with imageimpedancematching at their junctions,each of ,two adjacent ones of said half-sections havin both seriesandshunt-reactance arms of which each of two of said arms adjacent theirjunction includes a portion individually of the same reactance-frequencycharacteristic'and of inductive reactance at frequencies in the passband, a trap circuit included in each of said two adjacent halfsectionsand removed from said junction by at least one of said adjacentreactance arms and comprising the only other reactance of thehalfsection, one of said trap circuits comprising a shunt arm ofseries-connected capacitance and inductance resonant at a frequencyabove the pass band, and the other of said trap circuits comprising aseries arm having parallel-connected capacitance and inductance resonantat a frequency below the pass band, whereby the matched image impedanceat said junction is caused to have a maximum value at the lower cutofffrequency and a minimum value at the upper cutoff frequency of the passband and unlike trap circuits are provided in the said two adjacenthalf-sections.

3. A band-pass filter half-section having input and output pairs ofterminals and effectively comprising, seriesand shunt-reactance arms ofwhich each of at least two includes a portion individually of the samereactance-frequency characteristic. and of a given kind of reactance atfrequencies within the'pass band, and a trap circuit included in' one ofsaid reactance arms which is adjacent to one of said'pairs ofterminalsand which comprises the only other reactanceof said half-section, saidtrap circuit being resonant at a frequency outside of the pass band andhaving "in one of said reactance arms which is adjacent to one of saidpairs of terminals and comprising the only other reactance of saidhalf-section, said trap circuit being resonant at a frequency outside ofthe pass band and having capacitive reactance at frequencies withinthe'pass band,whereby the .image'impedance at the other of said pairs ofterminals is causedto'have a maximum value at the lower -cut-offfrequency and aminimum value at the upper cutoff frequency of the passband.

5.A- band-pass filter-'half-section having input and output pairs ofterminals and effectively comprising, seriesand shunt-reactance arms ofwhicheach of at least two includes a. portion individuallyhaving-aninductive reactance at frequencies' within the pass band, and atrap circuit comprising aseries-connected inductance and 'capacitance'resonant "at a frequency above the band and having capacitive'reactanceat frequencies within the pass band. said trap circuit being included inone of said shunt arms which is ada max mum value "at'the lower cutofffrequency and a minimum value at'the upper cutoff fre quency ofth'ep'ass band.

6. A band-pass filter half-section having input and output pairs ofterminals and effectively comprising, seriesand shunt-inductance arms ofwhich one is adjacent to one of said pairs of terminals, and ashunt-reactance arm across the other of said pairs of terminalsconsisting of a trap circuit comprising a series-connected inductanceand capacitance resonant at a frequency above the band, whereby theimage impedance at said one of said pairs of terminals is caused to havea maximum value at the lower cutoff frequency and a minimum value at theupper cutoff frequency of the pass band.

'7. A band-pass filter section having input and output pairs ofterminals and effectively comprising, two shunt arms each comprising asingle inductance connected across a different one of said pairs ofterminals, two series arms each including a single inductance, and ashunt arm between said series arms consisting of a trap circuitcomprising series-connected inductance and capacitance resonant at afrequency above the pass band, said trap circuit presenting capacitivereactance at frequencies within the ass band.

8. A band-pass filter half-section having input and output pairs ofterminals and effectively comprising, seriesand shunt-reactance arms ofwhich each of at least two includes a portion individually having aninductive reactance at frequencies in the pass 'band, and a trap circuitcomprising parallel-connected inductance and capacitance resonant at afrequency below said pass band and having capacitive reactance atfrequencies within the pass band, said trap circuit being included inone of said series-reactance arms which is adjacent to one of said pairsof terminals and comprising the only other reactance ofsaid'half-section, whereby the image impedance at the other of saidpairs of terminals is caused to have a maximum value at the lower cutofffrequency and a minimum value at the upper cutoff frequency of the passband.

9. A band-pass filter half-section having input and output pairs ofterminals and effectively comprising, seriesand shunt-reactance arms ofwhich each of at least two includes an inductance, and a trap circuitincluded in one of said quencies in the pass band, whereby the imageimpedance at the other of said pairs of terminals is caused to have amaximum value at the lower cutoff frequency and a minimum value at theupper cutoff frequency of the pass band.

10. A band-pass filter section having input and output pairs ofterminals and effectively comprising, two shunt-reactance arms eachincluding a single inductance and connected across a different one ofsaid pairs of terminals, a series-reactance arm between said shunt armsincluding in series an inductance and a trap circuit havingparallel-connected inductance and capacitance which is resonant at afrequency belowthe pass band and which has capacitive reactance atfrequencies within the pass band.

11. A band-pass filter half-section having inputand output pairs'ofterminals and effectively comprising, a series arm including inductance,a shunt arm including inductance, and a trap circuit included in one ofsaid arms and comprising the only other reactance of said half-section,said trap circuit being resonant at a frequency outside of the pass bandand having capacitive reactance at frequencies within the pass band,whereby the image impedance at the pair of said terminals furthestremoved from the 'arm including said trap circuit is caused to have amaximum value at the lower cutoff frequency and a minimum value at theupper cutoff frequency of the pass band.

12'. A band-pass filter section having input and output pairs ofterminals and effectively comprising, seriesand shunt-reactance arms ofwhich each of at leastthree includes a portion individually of the samereactance-frequency characteristic and of a :given kind of reactance atfrequencies'within the pass band, and a trap circuit included in'one ofsaid reactance arms which is between two of said three'reactance armsand comprising the only other reactance of said filter section, saidtrap circuit being resonant at a frequency outside of the pass bandandhaving reactance of the opposite kind at frequencies in the pass band,whereby the image impedance at both said pairs of terminals is caused tohave opposite extreme values at the respective cutoff frequencies ofth'e'pass band.

13. A band-pass filter section having input and output pairs ofterminals and comprising, seriesand shunt-reactance arms of .which'eachof at least three includes a portioniindividually having inductivereactance at frequencies within the pass band, anda trap'circuit'included'in one of said reactance arms which is between two ofsaid three reactance arms and comprising the only other reactance ofsaid 'filter section, said trap circuit being resonant at a frequencyoutside of the pass band and having'capacitive reactance at frequencieswithin the pass band, whereby the image impedance at both said pairs ofterminals is caused to have a maximum value at the lower cutofffrequency and 'a minimum value at the upper cutoff frequency of the passband.

14. A band-passfilter. section having input and output pairs ofterminals and effectively comprising, seriesand shunt reac'tance arms ofwhich each of at least three'in'cludes a portion individually-havinginductive reactance at frequencies within the pass band, and a trapcircuit comprising a series-connected inductance and capacitanceincluded in one 'of said shuntreactance arms which is between two ofsaid three reactance arms and comprising the only other reactance ofsaid filtersection, said trap circuit being resonant at 'a'frequencyabove the pass band and having capacitive reactance at frequencieswithin the'pass band, whereby the image impedance at both said pairs ofterminals is caused to have a maximum value at the lower cutofffrequency and a minimurn value at the upper cutoff frequency of the passband."

15. A band-pass'filter section having input and output pairs ofterminals and effectively comprising, seriesand shunt-reactance arms ofwhich each of at least three includes a portion individually havinginductive reactance at frequencies within the pass band, and a trapcircuit including a parallel-connected inductance and capacitanceincluded in one of said series arms whichis between two of said threereactance arms and comprising the only other reactance of said filtersection, said trap circuit being resonant at a frequency below the passband and having capacitive reactance at frequencies within the passband, whereby the image impedance at both said pairs of terminals iscaused to have a maximum value at the lower cutoff frequency and aminimum value at the upper cuto-fi frequency of the pass band.

16. A band-pass filter comprising, two resonant circuits each having aninductor coupled therewith by mutual inductance, a series circuitincluding said inductors and a trap circuit with parallel-connectedcapacitance and inductance resonant at a frequency below the pass band,and a second trap circuit connected in parallel with one of saidinductors including series-connected capacitance and inductance resonantat a frequency above the pass band, whereby a continuous band offrequencies is passed by said filter and maximum attenuation is securedat frequencies above and below the pass band.

1'7. A confluent band-pass filter comprising, two resonant circuits eachhaving an inductor coupled therewith by mutual inductance, a seriescircuit including said inductors and a trap circuit withparallel-connected capacitance and inductance resonant at a frequencybelow the pass band, and a second trap circuit connected in parallelwith one of said inductors including series-connected capacitance andinductance resonant at a frequency above the pass band, the reactiveconstants of the filter being proportioned to pass a single continuousband and to provide a band-pass constant-k form of image impedance ateach of said two resonant circuits.

18. A confluent band-pass filter comprising, two parallel-resonantcircuits each having an inductor coupled therewith by mutual inductance,a series circuit including said inductors and a trap circuit withparallel-connected capacitance and inductance resonant at a frequencybelow the pass band, and a second trap circuit connected in parallelwith one of said inductors including series-connected capacitance andinductance resonant at a frequency above the pass band, the reactiveconstants of the filter being proportioned to pass a single continuousband and to provide a band-pass constant-k mid-shunt form of imageimpedance across each of said two resonant circuits.

19. A band-pass filter comprising, a plurality of seriesandshunt-reactance arms, one said shunt arm including a trap circuit withseriesconnected inductance and capacitance resonant at a frequency onone side of the pass band, and an adjacent series arm including a trapcircuit with parallel-connected inductance and capacitance resonant at afrequency on the other side of the pass band, whereby said trap circuitsare caused to present reactance of opposite kind at frequencies withinthe pass band and to give maximum attenuation at frequencies above andbelow the pass band.

HAROLD A. WHEELER.

